Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,8,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(55.2921495107\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 6 x^{17} - 1798 x^{16} + 11087 x^{15} + 1326765 x^{14} - 8403720 x^{13} - 518334228 x^{12} + 3375594921 x^{11} + 115310342333 x^{10} + \cdots + 51\!\cdots\!48 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{5} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Root | \(8.74396\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 9.74396 | 0.861252 | 0.430626 | − | 0.902530i | \(-0.358293\pi\) | ||||
0.430626 | + | 0.902530i | \(0.358293\pi\) | |||||||
\(3\) | 27.0000 | 0.577350 | ||||||||
\(4\) | −33.0553 | −0.258245 | ||||||||
\(5\) | 321.882 | 1.15160 | 0.575800 | − | 0.817590i | \(-0.304691\pi\) | ||||
0.575800 | + | 0.817590i | \(0.304691\pi\) | |||||||
\(6\) | 263.087 | 0.497244 | ||||||||
\(7\) | −939.921 | −1.03573 | −0.517867 | − | 0.855461i | \(-0.673274\pi\) | ||||
−0.517867 | + | 0.855461i | \(0.673274\pi\) | |||||||
\(8\) | −1569.32 | −1.08367 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | 3136.41 | 0.991819 | ||||||||
\(11\) | 4998.14 | 1.13223 | 0.566114 | − | 0.824327i | \(-0.308446\pi\) | ||||
0.566114 | + | 0.824327i | \(0.308446\pi\) | |||||||
\(12\) | −892.494 | −0.149098 | ||||||||
\(13\) | −1233.64 | −0.155735 | −0.0778674 | − | 0.996964i | \(-0.524811\pi\) | ||||
−0.0778674 | + | 0.996964i | \(0.524811\pi\) | |||||||
\(14\) | −9158.55 | −0.892028 | ||||||||
\(15\) | 8690.82 | 0.664877 | ||||||||
\(16\) | −11060.3 | −0.675065 | ||||||||
\(17\) | 9783.69 | 0.482983 | 0.241491 | − | 0.970403i | \(-0.422363\pi\) | ||||
0.241491 | + | 0.970403i | \(0.422363\pi\) | |||||||
\(18\) | 7103.34 | 0.287084 | ||||||||
\(19\) | 19322.1 | 0.646275 | 0.323137 | − | 0.946352i | \(-0.395262\pi\) | ||||
0.323137 | + | 0.946352i | \(0.395262\pi\) | |||||||
\(20\) | −10639.9 | −0.297395 | ||||||||
\(21\) | −25377.9 | −0.597981 | ||||||||
\(22\) | 48701.6 | 0.975133 | ||||||||
\(23\) | 79805.1 | 1.36768 | 0.683838 | − | 0.729634i | \(-0.260310\pi\) | ||||
0.683838 | + | 0.729634i | \(0.260310\pi\) | |||||||
\(24\) | −42371.5 | −0.625655 | ||||||||
\(25\) | 25483.2 | 0.326184 | ||||||||
\(26\) | −12020.5 | −0.134127 | ||||||||
\(27\) | 19683.0 | 0.192450 | ||||||||
\(28\) | 31069.4 | 0.267473 | ||||||||
\(29\) | 144604. | 1.10100 | 0.550498 | − | 0.834836i | \(-0.314438\pi\) | ||||
0.550498 | + | 0.834836i | \(0.314438\pi\) | |||||||
\(30\) | 84683.0 | 0.572627 | ||||||||
\(31\) | 148320. | 0.894200 | 0.447100 | − | 0.894484i | \(-0.352457\pi\) | ||||
0.447100 | + | 0.894484i | \(0.352457\pi\) | |||||||
\(32\) | 93101.7 | 0.502265 | ||||||||
\(33\) | 134950. | 0.653692 | ||||||||
\(34\) | 95331.8 | 0.415970 | ||||||||
\(35\) | −302544. | −1.19275 | ||||||||
\(36\) | −24097.3 | −0.0860816 | ||||||||
\(37\) | 203959. | 0.661969 | 0.330985 | − | 0.943636i | \(-0.392619\pi\) | ||||
0.330985 | + | 0.943636i | \(0.392619\pi\) | |||||||
\(38\) | 188274. | 0.556605 | ||||||||
\(39\) | −33308.2 | −0.0899136 | ||||||||
\(40\) | −505135. | −1.24795 | ||||||||
\(41\) | −393071. | −0.890693 | −0.445346 | − | 0.895358i | \(-0.646919\pi\) | ||||
−0.445346 | + | 0.895358i | \(0.646919\pi\) | |||||||
\(42\) | −247281. | −0.515013 | ||||||||
\(43\) | 24364.6 | 0.0467325 | 0.0233663 | − | 0.999727i | \(-0.492562\pi\) | ||||
0.0233663 | + | 0.999727i | \(0.492562\pi\) | |||||||
\(44\) | −165215. | −0.292392 | ||||||||
\(45\) | 234652. | 0.383867 | ||||||||
\(46\) | 777617. | 1.17791 | ||||||||
\(47\) | −18634.3 | −0.0261800 | −0.0130900 | − | 0.999914i | \(-0.504167\pi\) | ||||
−0.0130900 | + | 0.999914i | \(0.504167\pi\) | |||||||
\(48\) | −298627. | −0.389749 | ||||||||
\(49\) | 59908.4 | 0.0727448 | ||||||||
\(50\) | 248307. | 0.280927 | ||||||||
\(51\) | 264160. | 0.278850 | ||||||||
\(52\) | 40778.3 | 0.0402177 | ||||||||
\(53\) | −228261. | −0.210603 | −0.105302 | − | 0.994440i | \(-0.533581\pi\) | ||||
−0.105302 | + | 0.994440i | \(0.533581\pi\) | |||||||
\(54\) | 191790. | 0.165748 | ||||||||
\(55\) | 1.60881e6 | 1.30387 | ||||||||
\(56\) | 1.47503e6 | 1.12239 | ||||||||
\(57\) | 521697. | 0.373127 | ||||||||
\(58\) | 1.40901e6 | 0.948235 | ||||||||
\(59\) | 205379. | 0.130189 | ||||||||
\(60\) | −287278. | −0.171701 | ||||||||
\(61\) | 2.54932e6 | 1.43804 | 0.719019 | − | 0.694991i | \(-0.244592\pi\) | ||||
0.719019 | + | 0.694991i | \(0.244592\pi\) | |||||||
\(62\) | 1.44523e6 | 0.770132 | ||||||||
\(63\) | −685202. | −0.345245 | ||||||||
\(64\) | 2.32289e6 | 1.10764 | ||||||||
\(65\) | −397086. | −0.179344 | ||||||||
\(66\) | 1.31494e6 | 0.562993 | ||||||||
\(67\) | 2.19172e6 | 0.890271 | 0.445136 | − | 0.895463i | \(-0.353155\pi\) | ||||
0.445136 | + | 0.895463i | \(0.353155\pi\) | |||||||
\(68\) | −323403. | −0.124728 | ||||||||
\(69\) | 2.15474e6 | 0.789628 | ||||||||
\(70\) | −2.94797e6 | −1.02726 | ||||||||
\(71\) | −3.19514e6 | −1.05946 | −0.529732 | − | 0.848165i | \(-0.677707\pi\) | ||||
−0.529732 | + | 0.848165i | \(0.677707\pi\) | |||||||
\(72\) | −1.14403e6 | −0.361222 | ||||||||
\(73\) | 2.62084e6 | 0.788516 | 0.394258 | − | 0.919000i | \(-0.371002\pi\) | ||||
0.394258 | + | 0.919000i | \(0.371002\pi\) | |||||||
\(74\) | 1.98737e6 | 0.570122 | ||||||||
\(75\) | 688045. | 0.188323 | ||||||||
\(76\) | −638699. | −0.166897 | ||||||||
\(77\) | −4.69785e6 | −1.17269 | ||||||||
\(78\) | −324554. | −0.0774382 | ||||||||
\(79\) | −2.93367e6 | −0.669448 | −0.334724 | − | 0.942316i | \(-0.608643\pi\) | ||||
−0.334724 | + | 0.942316i | \(0.608643\pi\) | |||||||
\(80\) | −3.56010e6 | −0.777405 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | −3.83007e6 | −0.767111 | ||||||||
\(83\) | −5.63931e6 | −1.08256 | −0.541280 | − | 0.840842i | \(-0.682060\pi\) | ||||
−0.541280 | + | 0.840842i | \(0.682060\pi\) | |||||||
\(84\) | 838873. | 0.154425 | ||||||||
\(85\) | 3.14920e6 | 0.556203 | ||||||||
\(86\) | 237407. | 0.0402485 | ||||||||
\(87\) | 3.90429e6 | 0.635661 | ||||||||
\(88\) | −7.84365e6 | −1.22696 | ||||||||
\(89\) | 8.11136e6 | 1.21963 | 0.609816 | − | 0.792543i | \(-0.291243\pi\) | ||||
0.609816 | + | 0.792543i | \(0.291243\pi\) | |||||||
\(90\) | 2.28644e6 | 0.330606 | ||||||||
\(91\) | 1.15952e6 | 0.161300 | ||||||||
\(92\) | −2.63798e6 | −0.353195 | ||||||||
\(93\) | 4.00465e6 | 0.516267 | ||||||||
\(94\) | −181571. | −0.0225476 | ||||||||
\(95\) | 6.21944e6 | 0.744250 | ||||||||
\(96\) | 2.51375e6 | 0.289983 | ||||||||
\(97\) | 6.86976e6 | 0.764259 | 0.382130 | − | 0.924109i | \(-0.375191\pi\) | ||||
0.382130 | + | 0.924109i | \(0.375191\pi\) | |||||||
\(98\) | 583745. | 0.0626516 | ||||||||
\(99\) | 3.64364e6 | 0.377409 | ||||||||
\(100\) | −842354. | −0.0842354 | ||||||||
\(101\) | 2.38664e6 | 0.230495 | 0.115248 | − | 0.993337i | \(-0.463234\pi\) | ||||
0.115248 | + | 0.993337i | \(0.463234\pi\) | |||||||
\(102\) | 2.57396e6 | 0.240160 | ||||||||
\(103\) | −1.07956e7 | −0.973456 | −0.486728 | − | 0.873553i | \(-0.661810\pi\) | ||||
−0.486728 | + | 0.873553i | \(0.661810\pi\) | |||||||
\(104\) | 1.93597e6 | 0.168765 | ||||||||
\(105\) | −8.16868e6 | −0.688636 | ||||||||
\(106\) | −2.22416e6 | −0.181383 | ||||||||
\(107\) | −7.34597e6 | −0.579703 | −0.289852 | − | 0.957072i | \(-0.593606\pi\) | ||||
−0.289852 | + | 0.957072i | \(0.593606\pi\) | |||||||
\(108\) | −650628. | −0.0496992 | ||||||||
\(109\) | 9.08395e6 | 0.671865 | 0.335933 | − | 0.941886i | \(-0.390949\pi\) | ||||
0.335933 | + | 0.941886i | \(0.390949\pi\) | |||||||
\(110\) | 1.56762e7 | 1.12296 | ||||||||
\(111\) | 5.50690e6 | 0.382188 | ||||||||
\(112\) | 1.03958e7 | 0.699188 | ||||||||
\(113\) | 2.23282e7 | 1.45573 | 0.727863 | − | 0.685722i | \(-0.240513\pi\) | ||||
0.727863 | + | 0.685722i | \(0.240513\pi\) | |||||||
\(114\) | 5.08339e6 | 0.321356 | ||||||||
\(115\) | 2.56878e7 | 1.57502 | ||||||||
\(116\) | −4.77992e6 | −0.284326 | ||||||||
\(117\) | −899322. | −0.0519116 | ||||||||
\(118\) | 2.00120e6 | 0.112125 | ||||||||
\(119\) | −9.19589e6 | −0.500241 | ||||||||
\(120\) | −1.36386e7 | −0.720505 | ||||||||
\(121\) | 5.49419e6 | 0.281939 | ||||||||
\(122\) | 2.48405e7 | 1.23851 | ||||||||
\(123\) | −1.06129e7 | −0.514242 | ||||||||
\(124\) | −4.90277e6 | −0.230922 | ||||||||
\(125\) | −1.69445e7 | −0.775967 | ||||||||
\(126\) | −6.67658e6 | −0.297343 | ||||||||
\(127\) | −6.47924e6 | −0.280680 | −0.140340 | − | 0.990103i | \(-0.544820\pi\) | ||||
−0.140340 | + | 0.990103i | \(0.544820\pi\) | |||||||
\(128\) | 1.07171e7 | 0.451694 | ||||||||
\(129\) | 657843. | 0.0269810 | ||||||||
\(130\) | −3.86919e6 | −0.154461 | ||||||||
\(131\) | 2.30891e7 | 0.897339 | 0.448670 | − | 0.893698i | \(-0.351898\pi\) | ||||
0.448670 | + | 0.893698i | \(0.351898\pi\) | |||||||
\(132\) | −4.46080e6 | −0.168812 | ||||||||
\(133\) | −1.81613e7 | −0.669368 | ||||||||
\(134\) | 2.13560e7 | 0.766748 | ||||||||
\(135\) | 6.33561e6 | 0.221626 | ||||||||
\(136\) | −1.53537e7 | −0.523392 | ||||||||
\(137\) | −4.31217e7 | −1.43276 | −0.716381 | − | 0.697709i | \(-0.754203\pi\) | ||||
−0.716381 | + | 0.697709i | \(0.754203\pi\) | |||||||
\(138\) | 2.09957e7 | 0.680069 | ||||||||
\(139\) | 1.97420e7 | 0.623504 | 0.311752 | − | 0.950163i | \(-0.399084\pi\) | ||||
0.311752 | + | 0.950163i | \(0.399084\pi\) | |||||||
\(140\) | 1.00007e7 | 0.308022 | ||||||||
\(141\) | −503125. | −0.0151150 | ||||||||
\(142\) | −3.11333e7 | −0.912465 | ||||||||
\(143\) | −6.16589e6 | −0.176327 | ||||||||
\(144\) | −8.06293e6 | −0.225022 | ||||||||
\(145\) | 4.65453e7 | 1.26791 | ||||||||
\(146\) | 2.55374e7 | 0.679111 | ||||||||
\(147\) | 1.61753e6 | 0.0419992 | ||||||||
\(148\) | −6.74194e6 | −0.170950 | ||||||||
\(149\) | −5.76420e7 | −1.42754 | −0.713768 | − | 0.700382i | \(-0.753013\pi\) | ||||
−0.713768 | + | 0.700382i | \(0.753013\pi\) | |||||||
\(150\) | 6.70428e6 | 0.162193 | ||||||||
\(151\) | 3.07490e7 | 0.726794 | 0.363397 | − | 0.931634i | \(-0.381617\pi\) | ||||
0.363397 | + | 0.931634i | \(0.381617\pi\) | |||||||
\(152\) | −3.03225e7 | −0.700346 | ||||||||
\(153\) | 7.13231e6 | 0.160994 | ||||||||
\(154\) | −4.57757e7 | −1.00998 | ||||||||
\(155\) | 4.77417e7 | 1.02976 | ||||||||
\(156\) | 1.10101e6 | 0.0232197 | ||||||||
\(157\) | 5.96166e6 | 0.122947 | 0.0614736 | − | 0.998109i | \(-0.480420\pi\) | ||||
0.0614736 | + | 0.998109i | \(0.480420\pi\) | |||||||
\(158\) | −2.85856e7 | −0.576564 | ||||||||
\(159\) | −6.16304e6 | −0.121592 | ||||||||
\(160\) | 2.99678e7 | 0.578409 | ||||||||
\(161\) | −7.50105e7 | −1.41655 | ||||||||
\(162\) | 5.17834e6 | 0.0956947 | ||||||||
\(163\) | 2.08332e7 | 0.376790 | 0.188395 | − | 0.982093i | \(-0.439671\pi\) | ||||
0.188395 | + | 0.982093i | \(0.439671\pi\) | |||||||
\(164\) | 1.29931e7 | 0.230017 | ||||||||
\(165\) | 4.34379e7 | 0.752792 | ||||||||
\(166\) | −5.49491e7 | −0.932358 | ||||||||
\(167\) | −4.41080e7 | −0.732840 | −0.366420 | − | 0.930449i | \(-0.619417\pi\) | ||||
−0.366420 | + | 0.930449i | \(0.619417\pi\) | |||||||
\(168\) | 3.98259e7 | 0.648012 | ||||||||
\(169\) | −6.12267e7 | −0.975747 | ||||||||
\(170\) | 3.06856e7 | 0.479031 | ||||||||
\(171\) | 1.40858e7 | 0.215425 | ||||||||
\(172\) | −805379. | −0.0120684 | ||||||||
\(173\) | −6.63421e7 | −0.974154 | −0.487077 | − | 0.873359i | \(-0.661937\pi\) | ||||
−0.487077 | + | 0.873359i | \(0.661937\pi\) | |||||||
\(174\) | 3.80433e7 | 0.547464 | ||||||||
\(175\) | −2.39522e7 | −0.337840 | ||||||||
\(176\) | −5.52807e7 | −0.764327 | ||||||||
\(177\) | 5.54523e6 | 0.0751646 | ||||||||
\(178\) | 7.90367e7 | 1.05041 | ||||||||
\(179\) | −1.18508e8 | −1.54441 | −0.772206 | − | 0.635372i | \(-0.780847\pi\) | ||||
−0.772206 | + | 0.635372i | \(0.780847\pi\) | |||||||
\(180\) | −7.75650e6 | −0.0991316 | ||||||||
\(181\) | −5.40992e7 | −0.678134 | −0.339067 | − | 0.940762i | \(-0.610111\pi\) | ||||
−0.339067 | + | 0.940762i | \(0.610111\pi\) | |||||||
\(182\) | 1.12983e7 | 0.138920 | ||||||||
\(183\) | 6.88317e7 | 0.830251 | ||||||||
\(184\) | −1.25239e8 | −1.48210 | ||||||||
\(185\) | 6.56509e7 | 0.762324 | ||||||||
\(186\) | 3.90211e7 | 0.444636 | ||||||||
\(187\) | 4.89002e7 | 0.546846 | ||||||||
\(188\) | 615961. | 0.00676084 | ||||||||
\(189\) | −1.85005e7 | −0.199327 | ||||||||
\(190\) | 6.06020e7 | 0.640987 | ||||||||
\(191\) | 8.73557e7 | 0.907140 | 0.453570 | − | 0.891221i | \(-0.350150\pi\) | ||||
0.453570 | + | 0.891221i | \(0.350150\pi\) | |||||||
\(192\) | 6.27181e7 | 0.639497 | ||||||||
\(193\) | −206564. | −0.00206826 | −0.00103413 | − | 0.999999i | \(-0.500329\pi\) | ||||
−0.00103413 | + | 0.999999i | \(0.500329\pi\) | |||||||
\(194\) | 6.69387e7 | 0.658220 | ||||||||
\(195\) | −1.07213e7 | −0.103545 | ||||||||
\(196\) | −1.98029e6 | −0.0187859 | ||||||||
\(197\) | −1.06894e8 | −0.996142 | −0.498071 | − | 0.867136i | \(-0.665958\pi\) | ||||
−0.498071 | + | 0.867136i | \(0.665958\pi\) | |||||||
\(198\) | 3.55035e7 | 0.325044 | ||||||||
\(199\) | −7.19278e7 | −0.647010 | −0.323505 | − | 0.946226i | \(-0.604861\pi\) | ||||
−0.323505 | + | 0.946226i | \(0.604861\pi\) | |||||||
\(200\) | −3.99911e7 | −0.353475 | ||||||||
\(201\) | 5.91763e7 | 0.513998 | ||||||||
\(202\) | 2.32553e7 | 0.198514 | ||||||||
\(203\) | −1.35916e8 | −1.14034 | ||||||||
\(204\) | −8.73188e6 | −0.0720116 | ||||||||
\(205\) | −1.26523e8 | −1.02572 | ||||||||
\(206\) | −1.05192e8 | −0.838391 | ||||||||
\(207\) | 5.81779e7 | 0.455892 | ||||||||
\(208\) | 1.36444e7 | 0.105131 | ||||||||
\(209\) | 9.65745e7 | 0.731730 | ||||||||
\(210\) | −7.95953e7 | −0.593089 | ||||||||
\(211\) | −1.64503e8 | −1.20555 | −0.602776 | − | 0.797910i | \(-0.705939\pi\) | ||||
−0.602776 | + | 0.797910i | \(0.705939\pi\) | |||||||
\(212\) | 7.54523e6 | 0.0543872 | ||||||||
\(213\) | −8.62688e7 | −0.611681 | ||||||||
\(214\) | −7.15788e7 | −0.499271 | ||||||||
\(215\) | 7.84252e6 | 0.0538172 | ||||||||
\(216\) | −3.08888e7 | −0.208552 | ||||||||
\(217\) | −1.39409e8 | −0.926153 | ||||||||
\(218\) | 8.85137e7 | 0.578645 | ||||||||
\(219\) | 7.07627e7 | 0.455250 | ||||||||
\(220\) | −5.31798e7 | −0.336718 | ||||||||
\(221\) | −1.20695e7 | −0.0752172 | ||||||||
\(222\) | 5.36590e7 | 0.329160 | ||||||||
\(223\) | −6.38980e7 | −0.385852 | −0.192926 | − | 0.981213i | \(-0.561798\pi\) | ||||
−0.192926 | + | 0.981213i | \(0.561798\pi\) | |||||||
\(224\) | −8.75082e7 | −0.520213 | ||||||||
\(225\) | 1.85772e7 | 0.108728 | ||||||||
\(226\) | 2.17565e8 | 1.25375 | ||||||||
\(227\) | 2.31309e8 | 1.31251 | 0.656256 | − | 0.754539i | \(-0.272139\pi\) | ||||
0.656256 | + | 0.754539i | \(0.272139\pi\) | |||||||
\(228\) | −1.72449e7 | −0.0963580 | ||||||||
\(229\) | −2.79302e8 | −1.53692 | −0.768458 | − | 0.639900i | \(-0.778976\pi\) | ||||
−0.768458 | + | 0.639900i | \(0.778976\pi\) | |||||||
\(230\) | 2.50301e8 | 1.35649 | ||||||||
\(231\) | −1.26842e8 | −0.677051 | ||||||||
\(232\) | −2.26929e8 | −1.19311 | ||||||||
\(233\) | 2.23510e8 | 1.15758 | 0.578790 | − | 0.815477i | \(-0.303525\pi\) | ||||
0.578790 | + | 0.815477i | \(0.303525\pi\) | |||||||
\(234\) | −8.76295e6 | −0.0447090 | ||||||||
\(235\) | −5.99803e6 | −0.0301489 | ||||||||
\(236\) | −6.78887e6 | −0.0336206 | ||||||||
\(237\) | −7.92092e7 | −0.386506 | ||||||||
\(238\) | −8.96044e7 | −0.430834 | ||||||||
\(239\) | 7.42988e7 | 0.352038 | 0.176019 | − | 0.984387i | \(-0.443678\pi\) | ||||
0.176019 | + | 0.984387i | \(0.443678\pi\) | |||||||
\(240\) | −9.61228e7 | −0.448835 | ||||||||
\(241\) | −1.59415e8 | −0.733615 | −0.366808 | − | 0.930297i | \(-0.619549\pi\) | ||||
−0.366808 | + | 0.930297i | \(0.619549\pi\) | |||||||
\(242\) | 5.35351e7 | 0.242820 | ||||||||
\(243\) | 1.43489e7 | 0.0641500 | ||||||||
\(244\) | −8.42686e7 | −0.371365 | ||||||||
\(245\) | 1.92835e7 | 0.0837729 | ||||||||
\(246\) | −1.03412e8 | −0.442892 | ||||||||
\(247\) | −2.38365e7 | −0.100647 | ||||||||
\(248\) | −2.32761e8 | −0.969014 | ||||||||
\(249\) | −1.52261e8 | −0.625017 | ||||||||
\(250\) | −1.65106e8 | −0.668303 | ||||||||
\(251\) | −1.11214e8 | −0.443918 | −0.221959 | − | 0.975056i | \(-0.571245\pi\) | ||||
−0.221959 | + | 0.975056i | \(0.571245\pi\) | |||||||
\(252\) | 2.26496e7 | 0.0891576 | ||||||||
\(253\) | 3.98877e8 | 1.54852 | ||||||||
\(254\) | −6.31334e7 | −0.241736 | ||||||||
\(255\) | 8.50283e7 | 0.321124 | ||||||||
\(256\) | −1.92903e8 | −0.718619 | ||||||||
\(257\) | −1.27820e8 | −0.469712 | −0.234856 | − | 0.972030i | \(-0.575462\pi\) | ||||
−0.234856 | + | 0.972030i | \(0.575462\pi\) | |||||||
\(258\) | 6.41000e6 | 0.0232375 | ||||||||
\(259\) | −1.91706e8 | −0.685624 | ||||||||
\(260\) | 1.31258e7 | 0.0463147 | ||||||||
\(261\) | 1.05416e8 | 0.366999 | ||||||||
\(262\) | 2.24979e8 | 0.772836 | ||||||||
\(263\) | 3.37653e8 | 1.14453 | 0.572263 | − | 0.820070i | \(-0.306066\pi\) | ||||
0.572263 | + | 0.820070i | \(0.306066\pi\) | |||||||
\(264\) | −2.11779e8 | −0.708383 | ||||||||
\(265\) | −7.34730e7 | −0.242531 | ||||||||
\(266\) | −1.76963e8 | −0.576495 | ||||||||
\(267\) | 2.19007e8 | 0.704154 | ||||||||
\(268\) | −7.24479e7 | −0.229908 | ||||||||
\(269\) | −3.70415e8 | −1.16026 | −0.580130 | − | 0.814524i | \(-0.696998\pi\) | ||||
−0.580130 | + | 0.814524i | \(0.696998\pi\) | |||||||
\(270\) | 6.17339e7 | 0.190876 | ||||||||
\(271\) | 2.34791e8 | 0.716619 | 0.358309 | − | 0.933603i | \(-0.383353\pi\) | ||||
0.358309 | + | 0.933603i | \(0.383353\pi\) | |||||||
\(272\) | −1.08210e8 | −0.326045 | ||||||||
\(273\) | 3.13071e7 | 0.0931265 | ||||||||
\(274\) | −4.20176e8 | −1.23397 | ||||||||
\(275\) | 1.27368e8 | 0.369315 | ||||||||
\(276\) | −7.12255e7 | −0.203917 | ||||||||
\(277\) | −1.55266e8 | −0.438932 | −0.219466 | − | 0.975620i | \(-0.570432\pi\) | ||||
−0.219466 | + | 0.975620i | \(0.570432\pi\) | |||||||
\(278\) | 1.92365e8 | 0.536994 | ||||||||
\(279\) | 1.08125e8 | 0.298067 | ||||||||
\(280\) | 4.74787e8 | 1.29254 | ||||||||
\(281\) | −1.15239e8 | −0.309834 | −0.154917 | − | 0.987927i | \(-0.549511\pi\) | ||||
−0.154917 | + | 0.987927i | \(0.549511\pi\) | |||||||
\(282\) | −4.90243e6 | −0.0130178 | ||||||||
\(283\) | 4.45082e8 | 1.16731 | 0.583657 | − | 0.812000i | \(-0.301621\pi\) | ||||
0.583657 | + | 0.812000i | \(0.301621\pi\) | |||||||
\(284\) | 1.05616e8 | 0.273601 | ||||||||
\(285\) | 1.67925e8 | 0.429693 | ||||||||
\(286\) | −6.00801e7 | −0.151862 | ||||||||
\(287\) | 3.69456e8 | 0.922521 | ||||||||
\(288\) | 6.78711e7 | 0.167422 | ||||||||
\(289\) | −3.14618e8 | −0.766728 | ||||||||
\(290\) | 4.53535e8 | 1.09199 | ||||||||
\(291\) | 1.85484e8 | 0.441245 | ||||||||
\(292\) | −8.66327e7 | −0.203630 | ||||||||
\(293\) | 7.32530e8 | 1.70133 | 0.850666 | − | 0.525707i | \(-0.176199\pi\) | ||||
0.850666 | + | 0.525707i | \(0.176199\pi\) | |||||||
\(294\) | 1.57611e7 | 0.0361719 | ||||||||
\(295\) | 6.61078e7 | 0.149926 | ||||||||
\(296\) | −3.20077e8 | −0.717353 | ||||||||
\(297\) | 9.83783e7 | 0.217897 | ||||||||
\(298\) | −5.61661e8 | −1.22947 | ||||||||
\(299\) | −9.84505e7 | −0.212995 | ||||||||
\(300\) | −2.27436e7 | −0.0486333 | ||||||||
\(301\) | −2.29008e7 | −0.0484024 | ||||||||
\(302\) | 2.99617e8 | 0.625953 | ||||||||
\(303\) | 6.44392e7 | 0.133076 | ||||||||
\(304\) | −2.13708e8 | −0.436277 | ||||||||
\(305\) | 8.20581e8 | 1.65604 | ||||||||
\(306\) | 6.94969e7 | 0.138657 | ||||||||
\(307\) | −2.59871e7 | −0.0512594 | −0.0256297 | − | 0.999672i | \(-0.508159\pi\) | ||||
−0.0256297 | + | 0.999672i | \(0.508159\pi\) | |||||||
\(308\) | 1.55289e8 | 0.302840 | ||||||||
\(309\) | −2.91481e8 | −0.562025 | ||||||||
\(310\) | 4.65193e8 | 0.886884 | ||||||||
\(311\) | 7.71976e8 | 1.45527 | 0.727633 | − | 0.685966i | \(-0.240620\pi\) | ||||
0.727633 | + | 0.685966i | \(0.240620\pi\) | |||||||
\(312\) | 5.22711e7 | 0.0974363 | ||||||||
\(313\) | −5.17834e8 | −0.954521 | −0.477261 | − | 0.878762i | \(-0.658370\pi\) | ||||
−0.477261 | + | 0.878762i | \(0.658370\pi\) | |||||||
\(314\) | 5.80901e7 | 0.105888 | ||||||||
\(315\) | −2.20554e8 | −0.397584 | ||||||||
\(316\) | 9.69735e7 | 0.172881 | ||||||||
\(317\) | 5.63749e8 | 0.993982 | 0.496991 | − | 0.867756i | \(-0.334438\pi\) | ||||
0.496991 | + | 0.867756i | \(0.334438\pi\) | |||||||
\(318\) | −6.00524e7 | −0.104721 | ||||||||
\(319\) | 7.22748e8 | 1.24658 | ||||||||
\(320\) | 7.47698e8 | 1.27556 | ||||||||
\(321\) | −1.98341e8 | −0.334692 | ||||||||
\(322\) | −7.30899e8 | −1.22000 | ||||||||
\(323\) | 1.89042e8 | 0.312139 | ||||||||
\(324\) | −1.75670e7 | −0.0286939 | ||||||||
\(325\) | −3.14370e7 | −0.0507983 | ||||||||
\(326\) | 2.02998e8 | 0.324511 | ||||||||
\(327\) | 2.45267e8 | 0.387902 | ||||||||
\(328\) | 6.16853e8 | 0.965213 | ||||||||
\(329\) | 1.75147e7 | 0.0271155 | ||||||||
\(330\) | 4.23257e8 | 0.648344 | ||||||||
\(331\) | −4.79482e8 | −0.726733 | −0.363366 | − | 0.931646i | \(-0.618373\pi\) | ||||
−0.363366 | + | 0.931646i | \(0.618373\pi\) | |||||||
\(332\) | 1.86409e8 | 0.279566 | ||||||||
\(333\) | 1.48686e8 | 0.220656 | ||||||||
\(334\) | −4.29786e8 | −0.631160 | ||||||||
\(335\) | 7.05474e8 | 1.02524 | ||||||||
\(336\) | 2.80686e8 | 0.403676 | ||||||||
\(337\) | 3.39194e8 | 0.482773 | 0.241387 | − | 0.970429i | \(-0.422398\pi\) | ||||
0.241387 | + | 0.970429i | \(0.422398\pi\) | |||||||
\(338\) | −5.96590e8 | −0.840364 | ||||||||
\(339\) | 6.02862e8 | 0.840464 | ||||||||
\(340\) | −1.04098e8 | −0.143636 | ||||||||
\(341\) | 7.41325e8 | 1.01244 | ||||||||
\(342\) | 1.37252e8 | 0.185535 | ||||||||
\(343\) | 7.17756e8 | 0.960390 | ||||||||
\(344\) | −3.82357e7 | −0.0506424 | ||||||||
\(345\) | 6.93571e8 | 0.909336 | ||||||||
\(346\) | −6.46434e8 | −0.838992 | ||||||||
\(347\) | 9.78350e8 | 1.25702 | 0.628508 | − | 0.777803i | \(-0.283666\pi\) | ||||
0.628508 | + | 0.777803i | \(0.283666\pi\) | |||||||
\(348\) | −1.29058e8 | −0.164156 | ||||||||
\(349\) | −2.36450e8 | −0.297749 | −0.148875 | − | 0.988856i | \(-0.547565\pi\) | ||||
−0.148875 | + | 0.988856i | \(0.547565\pi\) | |||||||
\(350\) | −2.33389e8 | −0.290966 | ||||||||
\(351\) | −2.42817e7 | −0.0299712 | ||||||||
\(352\) | 4.65335e8 | 0.568678 | ||||||||
\(353\) | −1.61081e8 | −0.194910 | −0.0974548 | − | 0.995240i | \(-0.531070\pi\) | ||||
−0.0974548 | + | 0.995240i | \(0.531070\pi\) | |||||||
\(354\) | 5.40325e7 | 0.0647357 | ||||||||
\(355\) | −1.02846e9 | −1.22008 | ||||||||
\(356\) | −2.68124e8 | −0.314963 | ||||||||
\(357\) | −2.48289e8 | −0.288814 | ||||||||
\(358\) | −1.15474e9 | −1.33013 | ||||||||
\(359\) | −1.10346e9 | −1.25871 | −0.629355 | − | 0.777118i | \(-0.716681\pi\) | ||||
−0.629355 | + | 0.777118i | \(0.716681\pi\) | |||||||
\(360\) | −3.68243e8 | −0.415984 | ||||||||
\(361\) | −5.20528e8 | −0.582329 | ||||||||
\(362\) | −5.27140e8 | −0.584044 | ||||||||
\(363\) | 1.48343e8 | 0.162777 | ||||||||
\(364\) | −3.83284e7 | −0.0416548 | ||||||||
\(365\) | 8.43602e8 | 0.908056 | ||||||||
\(366\) | 6.70693e8 | 0.715056 | ||||||||
\(367\) | −1.44038e8 | −0.152105 | −0.0760527 | − | 0.997104i | \(-0.524232\pi\) | ||||
−0.0760527 | + | 0.997104i | \(0.524232\pi\) | |||||||
\(368\) | −8.82665e8 | −0.923270 | ||||||||
\(369\) | −2.86549e8 | −0.296898 | ||||||||
\(370\) | 6.39700e8 | 0.656553 | ||||||||
\(371\) | 2.14547e8 | 0.218129 | ||||||||
\(372\) | −1.32375e8 | −0.133323 | ||||||||
\(373\) | 1.06553e9 | 1.06312 | 0.531561 | − | 0.847020i | \(-0.321606\pi\) | ||||
0.531561 | + | 0.847020i | \(0.321606\pi\) | |||||||
\(374\) | 4.76481e8 | 0.470972 | ||||||||
\(375\) | −4.57501e8 | −0.448004 | ||||||||
\(376\) | 2.92430e7 | 0.0283704 | ||||||||
\(377\) | −1.78388e8 | −0.171463 | ||||||||
\(378\) | −1.80268e8 | −0.171671 | ||||||||
\(379\) | 1.49139e9 | 1.40719 | 0.703597 | − | 0.710600i | \(-0.251576\pi\) | ||||
0.703597 | + | 0.710600i | \(0.251576\pi\) | |||||||
\(380\) | −2.05586e8 | −0.192199 | ||||||||
\(381\) | −1.74939e8 | −0.162051 | ||||||||
\(382\) | 8.51190e8 | 0.781276 | ||||||||
\(383\) | −1.49307e9 | −1.35795 | −0.678976 | − | 0.734160i | \(-0.737576\pi\) | ||||
−0.678976 | + | 0.734160i | \(0.737576\pi\) | |||||||
\(384\) | 2.89363e8 | 0.260786 | ||||||||
\(385\) | −1.51216e9 | −1.35047 | ||||||||
\(386\) | −2.01275e6 | −0.00178129 | ||||||||
\(387\) | 1.77618e7 | 0.0155775 | ||||||||
\(388\) | −2.27082e8 | −0.197366 | ||||||||
\(389\) | 7.33205e8 | 0.631541 | 0.315771 | − | 0.948836i | \(-0.397737\pi\) | ||||
0.315771 | + | 0.948836i | \(0.397737\pi\) | |||||||
\(390\) | −1.04468e8 | −0.0891779 | ||||||||
\(391\) | 7.80788e8 | 0.660563 | ||||||||
\(392\) | −9.40153e7 | −0.0788310 | ||||||||
\(393\) | 6.23405e8 | 0.518079 | ||||||||
\(394\) | −1.04157e9 | −0.857930 | ||||||||
\(395\) | −9.44297e8 | −0.770937 | ||||||||
\(396\) | −1.20442e8 | −0.0974639 | ||||||||
\(397\) | −2.09263e9 | −1.67851 | −0.839257 | − | 0.543735i | \(-0.817010\pi\) | ||||
−0.839257 | + | 0.543735i | \(0.817010\pi\) | |||||||
\(398\) | −7.00861e8 | −0.557239 | ||||||||
\(399\) | −4.90354e8 | −0.386460 | ||||||||
\(400\) | −2.81851e8 | −0.220196 | ||||||||
\(401\) | −1.30799e9 | −1.01298 | −0.506489 | − | 0.862247i | \(-0.669057\pi\) | ||||
−0.506489 | + | 0.862247i | \(0.669057\pi\) | |||||||
\(402\) | 5.76612e8 | 0.442682 | ||||||||
\(403\) | −1.82973e8 | −0.139258 | ||||||||
\(404\) | −7.88910e7 | −0.0595241 | ||||||||
\(405\) | 1.71061e8 | 0.127956 | ||||||||
\(406\) | −1.32436e9 | −0.982120 | ||||||||
\(407\) | 1.01942e9 | 0.749499 | ||||||||
\(408\) | −4.14550e8 | −0.302180 | ||||||||
\(409\) | 2.74486e9 | 1.98376 | 0.991878 | − | 0.127193i | \(-0.0405967\pi\) | ||||
0.991878 | + | 0.127193i | \(0.0405967\pi\) | |||||||
\(410\) | −1.23283e9 | −0.883406 | ||||||||
\(411\) | −1.16429e9 | −0.827206 | ||||||||
\(412\) | 3.56852e8 | 0.251390 | ||||||||
\(413\) | −1.93040e8 | −0.134841 | ||||||||
\(414\) | 5.66883e8 | 0.392638 | ||||||||
\(415\) | −1.81519e9 | −1.24668 | ||||||||
\(416\) | −1.14854e8 | −0.0782201 | ||||||||
\(417\) | 5.33034e8 | 0.359980 | ||||||||
\(418\) | 9.41018e8 | 0.630204 | ||||||||
\(419\) | −6.51049e7 | −0.0432379 | −0.0216189 | − | 0.999766i | \(-0.506882\pi\) | ||||
−0.0216189 | + | 0.999766i | \(0.506882\pi\) | |||||||
\(420\) | 2.70018e8 | 0.177837 | ||||||||
\(421\) | 1.48843e9 | 0.972170 | 0.486085 | − | 0.873912i | \(-0.338425\pi\) | ||||
0.486085 | + | 0.873912i | \(0.338425\pi\) | |||||||
\(422\) | −1.60291e9 | −1.03828 | ||||||||
\(423\) | −1.35844e7 | −0.00872666 | ||||||||
\(424\) | 3.58213e8 | 0.228224 | ||||||||
\(425\) | 2.49319e8 | 0.157541 | ||||||||
\(426\) | −8.40600e8 | −0.526812 | ||||||||
\(427\) | −2.39616e9 | −1.48942 | ||||||||
\(428\) | 2.42823e8 | 0.149705 | ||||||||
\(429\) | −1.66479e8 | −0.101803 | ||||||||
\(430\) | 7.64172e7 | 0.0463502 | ||||||||
\(431\) | 1.85011e9 | 1.11308 | 0.556540 | − | 0.830821i | \(-0.312129\pi\) | ||||
0.556540 | + | 0.830821i | \(0.312129\pi\) | |||||||
\(432\) | −2.17699e8 | −0.129916 | ||||||||
\(433\) | 6.17068e8 | 0.365280 | 0.182640 | − | 0.983180i | \(-0.441536\pi\) | ||||
0.182640 | + | 0.983180i | \(0.441536\pi\) | |||||||
\(434\) | −1.35840e9 | −0.797651 | ||||||||
\(435\) | 1.25672e9 | 0.732027 | ||||||||
\(436\) | −3.00273e8 | −0.173506 | ||||||||
\(437\) | 1.54200e9 | 0.883894 | ||||||||
\(438\) | 6.89509e8 | 0.392085 | ||||||||
\(439\) | −7.44414e8 | −0.419941 | −0.209971 | − | 0.977708i | \(-0.567337\pi\) | ||||
−0.209971 | + | 0.977708i | \(0.567337\pi\) | |||||||
\(440\) | −2.52473e9 | −1.41296 | ||||||||
\(441\) | 4.36733e7 | 0.0242483 | ||||||||
\(442\) | −1.17605e8 | −0.0647810 | ||||||||
\(443\) | −1.54073e9 | −0.842004 | −0.421002 | − | 0.907060i | \(-0.638321\pi\) | ||||
−0.421002 | + | 0.907060i | \(0.638321\pi\) | |||||||
\(444\) | −1.82032e8 | −0.0986980 | ||||||||
\(445\) | 2.61090e9 | 1.40453 | ||||||||
\(446\) | −6.22619e8 | −0.332316 | ||||||||
\(447\) | −1.55633e9 | −0.824188 | ||||||||
\(448\) | −2.18334e9 | −1.14722 | ||||||||
\(449\) | −3.21711e8 | −0.167727 | −0.0838636 | − | 0.996477i | \(-0.526726\pi\) | ||||
−0.0838636 | + | 0.996477i | \(0.526726\pi\) | |||||||
\(450\) | 1.81016e8 | 0.0936424 | ||||||||
\(451\) | −1.96462e9 | −1.00847 | ||||||||
\(452\) | −7.38067e8 | −0.375934 | ||||||||
\(453\) | 8.30222e8 | 0.419615 | ||||||||
\(454\) | 2.25387e9 | 1.13040 | ||||||||
\(455\) | 3.73229e8 | 0.185753 | ||||||||
\(456\) | −8.18708e8 | −0.404345 | ||||||||
\(457\) | −1.64590e9 | −0.806673 | −0.403336 | − | 0.915052i | \(-0.632150\pi\) | ||||
−0.403336 | + | 0.915052i | \(0.632150\pi\) | |||||||
\(458\) | −2.72151e9 | −1.32367 | ||||||||
\(459\) | 1.92572e8 | 0.0929500 | ||||||||
\(460\) | −8.49119e8 | −0.406740 | ||||||||
\(461\) | 1.86228e9 | 0.885301 | 0.442650 | − | 0.896694i | \(-0.354038\pi\) | ||||
0.442650 | + | 0.896694i | \(0.354038\pi\) | |||||||
\(462\) | −1.23594e9 | −0.583111 | ||||||||
\(463\) | 1.30026e9 | 0.608833 | 0.304417 | − | 0.952539i | \(-0.401538\pi\) | ||||
0.304417 | + | 0.952539i | \(0.401538\pi\) | |||||||
\(464\) | −1.59935e9 | −0.743244 | ||||||||
\(465\) | 1.28902e9 | 0.594533 | ||||||||
\(466\) | 2.17787e9 | 0.996969 | ||||||||
\(467\) | 2.19765e9 | 0.998501 | 0.499251 | − | 0.866458i | \(-0.333609\pi\) | ||||
0.499251 | + | 0.866458i | \(0.333609\pi\) | |||||||
\(468\) | 2.97274e7 | 0.0134059 | ||||||||
\(469\) | −2.06004e9 | −0.922084 | ||||||||
\(470\) | −5.84446e7 | −0.0259658 | ||||||||
\(471\) | 1.60965e8 | 0.0709836 | ||||||||
\(472\) | −3.22305e8 | −0.141081 | ||||||||
\(473\) | 1.21777e8 | 0.0529118 | ||||||||
\(474\) | −7.71811e8 | −0.332879 | ||||||||
\(475\) | 4.92389e8 | 0.210805 | ||||||||
\(476\) | 3.03973e8 | 0.129185 | ||||||||
\(477\) | −1.66402e8 | −0.0702011 | ||||||||
\(478\) | 7.23964e8 | 0.303193 | ||||||||
\(479\) | −4.13730e9 | −1.72006 | −0.860029 | − | 0.510245i | \(-0.829555\pi\) | ||||
−0.860029 | + | 0.510245i | \(0.829555\pi\) | |||||||
\(480\) | 8.09130e8 | 0.333944 | ||||||||
\(481\) | −2.51612e8 | −0.103092 | ||||||||
\(482\) | −1.55333e9 | −0.631828 | ||||||||
\(483\) | −2.02528e9 | −0.817844 | ||||||||
\(484\) | −1.81612e8 | −0.0728092 | ||||||||
\(485\) | 2.21125e9 | 0.880121 | ||||||||
\(486\) | 1.39815e8 | 0.0552494 | ||||||||
\(487\) | 5.06252e9 | 1.98617 | 0.993083 | − | 0.117413i | \(-0.0374601\pi\) | ||||
0.993083 | + | 0.117413i | \(0.0374601\pi\) | |||||||
\(488\) | −4.00069e9 | −1.55835 | ||||||||
\(489\) | 5.62496e8 | 0.217540 | ||||||||
\(490\) | 1.87897e8 | 0.0721496 | ||||||||
\(491\) | 5.29752e8 | 0.201970 | 0.100985 | − | 0.994888i | \(-0.467801\pi\) | ||||
0.100985 | + | 0.994888i | \(0.467801\pi\) | |||||||
\(492\) | 3.50814e8 | 0.132800 | ||||||||
\(493\) | 1.41476e9 | 0.531762 | ||||||||
\(494\) | −2.32262e8 | −0.0866828 | ||||||||
\(495\) | 1.17282e9 | 0.434625 | ||||||||
\(496\) | −1.64046e9 | −0.603643 | ||||||||
\(497\) | 3.00318e9 | 1.09732 | ||||||||
\(498\) | −1.48363e9 | −0.538297 | ||||||||
\(499\) | 1.14827e9 | 0.413705 | 0.206852 | − | 0.978372i | \(-0.433678\pi\) | ||||
0.206852 | + | 0.978372i | \(0.433678\pi\) | |||||||
\(500\) | 5.60105e8 | 0.200389 | ||||||||
\(501\) | −1.19092e9 | −0.423106 | ||||||||
\(502\) | −1.08367e9 | −0.382326 | ||||||||
\(503\) | 2.33999e9 | 0.819835 | 0.409918 | − | 0.912123i | \(-0.365557\pi\) | ||||
0.409918 | + | 0.912123i | \(0.365557\pi\) | |||||||
\(504\) | 1.07530e9 | 0.374130 | ||||||||
\(505\) | 7.68216e8 | 0.265438 | ||||||||
\(506\) | 3.88664e9 | 1.33367 | ||||||||
\(507\) | −1.65312e9 | −0.563348 | ||||||||
\(508\) | 2.14173e8 | 0.0724840 | ||||||||
\(509\) | 3.44383e9 | 1.15752 | 0.578762 | − | 0.815497i | \(-0.303536\pi\) | ||||
0.578762 | + | 0.815497i | \(0.303536\pi\) | |||||||
\(510\) | 8.28512e8 | 0.276569 | ||||||||
\(511\) | −2.46338e9 | −0.816693 | ||||||||
\(512\) | −3.25143e9 | −1.07061 | ||||||||
\(513\) | 3.80317e8 | 0.124376 | ||||||||
\(514\) | −1.24547e9 | −0.404540 | ||||||||
\(515\) | −3.47491e9 | −1.12103 | ||||||||
\(516\) | −2.17452e7 | −0.00696771 | ||||||||
\(517\) | −9.31365e7 | −0.0296417 | ||||||||
\(518\) | −1.86797e9 | −0.590495 | ||||||||
\(519\) | −1.79124e9 | −0.562428 | ||||||||
\(520\) | 6.23153e8 | 0.194349 | ||||||||
\(521\) | −5.23947e9 | −1.62314 | −0.811568 | − | 0.584258i | \(-0.801386\pi\) | ||||
−0.811568 | + | 0.584258i | \(0.801386\pi\) | |||||||
\(522\) | 1.02717e9 | 0.316078 | ||||||||
\(523\) | 1.85224e9 | 0.566164 | 0.283082 | − | 0.959096i | \(-0.408643\pi\) | ||||
0.283082 | + | 0.959096i | \(0.408643\pi\) | |||||||
\(524\) | −7.63216e8 | −0.231733 | ||||||||
\(525\) | −6.46708e8 | −0.195052 | ||||||||
\(526\) | 3.29008e9 | 0.985725 | ||||||||
\(527\) | 1.45112e9 | 0.431883 | ||||||||
\(528\) | −1.49258e9 | −0.441284 | ||||||||
\(529\) | 2.96402e9 | 0.870536 | ||||||||
\(530\) | −7.15918e8 | −0.208880 | ||||||||
\(531\) | 1.49721e8 | 0.0433963 | ||||||||
\(532\) | 6.00326e8 | 0.172861 | ||||||||
\(533\) | 4.84908e8 | 0.138712 | ||||||||
\(534\) | 2.13399e9 | 0.606455 | ||||||||
\(535\) | −2.36454e9 | −0.667587 | ||||||||
\(536\) | −3.43949e9 | −0.964757 | ||||||||
\(537\) | −3.19972e9 | −0.891667 | ||||||||
\(538\) | −3.60931e9 | −0.999277 | ||||||||
\(539\) | 2.99431e8 | 0.0823636 | ||||||||
\(540\) | −2.09426e8 | −0.0572337 | ||||||||
\(541\) | 7.04253e8 | 0.191222 | 0.0956111 | − | 0.995419i | \(-0.469519\pi\) | ||||
0.0956111 | + | 0.995419i | \(0.469519\pi\) | |||||||
\(542\) | 2.28779e9 | 0.617190 | ||||||||
\(543\) | −1.46068e9 | −0.391521 | ||||||||
\(544\) | 9.10878e8 | 0.242585 | ||||||||
\(545\) | 2.92396e9 | 0.773721 | ||||||||
\(546\) | 3.05055e8 | 0.0802054 | ||||||||
\(547\) | 3.55125e9 | 0.927738 | 0.463869 | − | 0.885904i | \(-0.346461\pi\) | ||||
0.463869 | + | 0.885904i | \(0.346461\pi\) | |||||||
\(548\) | 1.42540e9 | 0.370003 | ||||||||
\(549\) | 1.85846e9 | 0.479346 | ||||||||
\(550\) | 1.24107e9 | 0.318073 | ||||||||
\(551\) | 2.79405e9 | 0.711546 | ||||||||
\(552\) | −3.38146e9 | −0.855693 | ||||||||
\(553\) | 2.75742e9 | 0.693370 | ||||||||
\(554\) | −1.51291e9 | −0.378032 | ||||||||
\(555\) | 1.77257e9 | 0.440128 | ||||||||
\(556\) | −6.52578e8 | −0.161017 | ||||||||
\(557\) | −1.10300e9 | −0.270447 | −0.135223 | − | 0.990815i | \(-0.543175\pi\) | ||||
−0.135223 | + | 0.990815i | \(0.543175\pi\) | |||||||
\(558\) | 1.05357e9 | 0.256711 | ||||||||
\(559\) | −3.00570e7 | −0.00727788 | ||||||||
\(560\) | 3.34622e9 | 0.805185 | ||||||||
\(561\) | 1.32031e9 | 0.315722 | ||||||||
\(562\) | −1.12289e9 | −0.266845 | ||||||||
\(563\) | 5.07113e8 | 0.119764 | 0.0598818 | − | 0.998205i | \(-0.480928\pi\) | ||||
0.0598818 | + | 0.998205i | \(0.480928\pi\) | |||||||
\(564\) | 1.66309e7 | 0.00390337 | ||||||||
\(565\) | 7.18706e9 | 1.67642 | ||||||||
\(566\) | 4.33686e9 | 1.00535 | ||||||||
\(567\) | −4.99513e8 | −0.115082 | ||||||||
\(568\) | 5.01419e9 | 1.14810 | ||||||||
\(569\) | −6.60666e9 | −1.50345 | −0.751726 | − | 0.659476i | \(-0.770778\pi\) | ||||
−0.751726 | + | 0.659476i | \(0.770778\pi\) | |||||||
\(570\) | 1.63625e9 | 0.370074 | ||||||||
\(571\) | 3.31524e9 | 0.745227 | 0.372613 | − | 0.927987i | \(-0.378462\pi\) | ||||
0.372613 | + | 0.927987i | \(0.378462\pi\) | |||||||
\(572\) | 2.03815e8 | 0.0455356 | ||||||||
\(573\) | 2.35860e9 | 0.523737 | ||||||||
\(574\) | 3.59996e9 | 0.794523 | ||||||||
\(575\) | 2.03369e9 | 0.446114 | ||||||||
\(576\) | 1.69339e9 | 0.369214 | ||||||||
\(577\) | −6.56723e9 | −1.42320 | −0.711601 | − | 0.702584i | \(-0.752030\pi\) | ||||
−0.711601 | + | 0.702584i | \(0.752030\pi\) | |||||||
\(578\) | −3.06562e9 | −0.660346 | ||||||||
\(579\) | −5.57723e6 | −0.00119411 | ||||||||
\(580\) | −1.53857e9 | −0.327431 | ||||||||
\(581\) | 5.30050e9 | 1.12125 | ||||||||
\(582\) | 1.80734e9 | 0.380023 | ||||||||
\(583\) | −1.14088e9 | −0.238451 | ||||||||
\(584\) | −4.11293e9 | −0.854488 | ||||||||
\(585\) | −2.89476e8 | −0.0597815 | ||||||||
\(586\) | 7.13774e9 | 1.46528 | ||||||||
\(587\) | −2.12865e9 | −0.434380 | −0.217190 | − | 0.976129i | \(-0.569689\pi\) | ||||
−0.217190 | + | 0.976129i | \(0.569689\pi\) | |||||||
\(588\) | −5.34679e7 | −0.0108461 | ||||||||
\(589\) | 2.86586e9 | 0.577899 | ||||||||
\(590\) | 6.44152e8 | 0.129124 | ||||||||
\(591\) | −2.88614e9 | −0.575123 | ||||||||
\(592\) | −2.25585e9 | −0.446872 | ||||||||
\(593\) | 6.79461e7 | 0.0133805 | 0.00669026 | − | 0.999978i | \(-0.497870\pi\) | ||||
0.00669026 | + | 0.999978i | \(0.497870\pi\) | |||||||
\(594\) | 9.58594e8 | 0.187664 | ||||||||
\(595\) | −2.95999e9 | −0.576078 | ||||||||
\(596\) | 1.90537e9 | 0.368653 | ||||||||
\(597\) | −1.94205e9 | −0.373551 | ||||||||
\(598\) | −9.59297e8 | −0.183442 | ||||||||
\(599\) | −3.92845e9 | −0.746840 | −0.373420 | − | 0.927662i | \(-0.621815\pi\) | ||||
−0.373420 | + | 0.927662i | \(0.621815\pi\) | |||||||
\(600\) | −1.07976e9 | −0.204079 | ||||||||
\(601\) | −5.25955e9 | −0.988298 | −0.494149 | − | 0.869377i | \(-0.664520\pi\) | ||||
−0.494149 | + | 0.869377i | \(0.664520\pi\) | |||||||
\(602\) | −2.23144e8 | −0.0416867 | ||||||||
\(603\) | 1.59776e9 | 0.296757 | ||||||||
\(604\) | −1.01642e9 | −0.187691 | ||||||||
\(605\) | 1.76848e9 | 0.324681 | ||||||||
\(606\) | 6.27893e8 | 0.114612 | ||||||||
\(607\) | −7.11758e9 | −1.29173 | −0.645865 | − | 0.763452i | \(-0.723503\pi\) | ||||
−0.645865 | + | 0.763452i | \(0.723503\pi\) | |||||||
\(608\) | 1.79892e9 | 0.324601 | ||||||||
\(609\) | −3.66973e9 | −0.658375 | ||||||||
\(610\) | 7.99571e9 | 1.42627 | ||||||||
\(611\) | 2.29879e7 | 0.00407714 | ||||||||
\(612\) | −2.35761e8 | −0.0415759 | ||||||||
\(613\) | −8.31463e9 | −1.45791 | −0.728956 | − | 0.684561i | \(-0.759994\pi\) | ||||
−0.728956 | + | 0.684561i | \(0.759994\pi\) | |||||||
\(614\) | −2.53217e8 | −0.0441473 | ||||||||
\(615\) | −3.41611e9 | −0.592201 | ||||||||
\(616\) | 7.37241e9 | 1.27080 | ||||||||
\(617\) | −8.10336e9 | −1.38889 | −0.694444 | − | 0.719547i | \(-0.744349\pi\) | ||||
−0.694444 | + | 0.719547i | \(0.744349\pi\) | |||||||
\(618\) | −2.84018e9 | −0.484046 | ||||||||
\(619\) | 6.25611e8 | 0.106020 | 0.0530099 | − | 0.998594i | \(-0.483119\pi\) | ||||
0.0530099 | + | 0.998594i | \(0.483119\pi\) | |||||||
\(620\) | −1.57812e9 | −0.265930 | ||||||||
\(621\) | 1.57080e9 | 0.263209 | ||||||||
\(622\) | 7.52210e9 | 1.25335 | ||||||||
\(623\) | −7.62404e9 | −1.26321 | ||||||||
\(624\) | 3.68398e8 | 0.0606975 | ||||||||
\(625\) | −7.44500e9 | −1.21979 | ||||||||
\(626\) | −5.04575e9 | −0.822083 | ||||||||
\(627\) | 2.60751e9 | 0.422464 | ||||||||
\(628\) | −1.97065e8 | −0.0317504 | ||||||||
\(629\) | 1.99548e9 | 0.319719 | ||||||||
\(630\) | −2.14907e9 | −0.342420 | ||||||||
\(631\) | −5.93874e9 | −0.941004 | −0.470502 | − | 0.882399i | \(-0.655927\pi\) | ||||
−0.470502 | + | 0.882399i | \(0.655927\pi\) | |||||||
\(632\) | 4.60386e9 | 0.725458 | ||||||||
\(633\) | −4.44159e9 | −0.696026 | ||||||||
\(634\) | 5.49315e9 | 0.856070 | ||||||||
\(635\) | −2.08555e9 | −0.323231 | ||||||||
\(636\) | 2.03721e8 | 0.0314005 | ||||||||
\(637\) | −7.39053e7 | −0.0113289 | ||||||||
\(638\) | 7.04242e9 | 1.07362 | ||||||||
\(639\) | −2.32926e9 | −0.353154 | ||||||||
\(640\) | 3.44966e9 | 0.520171 | ||||||||
\(641\) | 7.93154e9 | 1.18947 | 0.594736 | − | 0.803921i | \(-0.297257\pi\) | ||||
0.594736 | + | 0.803921i | \(0.297257\pi\) | |||||||
\(642\) | −1.93263e9 | −0.288254 | ||||||||
\(643\) | 1.20200e9 | 0.178306 | 0.0891530 | − | 0.996018i | \(-0.471584\pi\) | ||||
0.0891530 | + | 0.996018i | \(0.471584\pi\) | |||||||
\(644\) | 2.47949e9 | 0.365816 | ||||||||
\(645\) | 2.11748e8 | 0.0310714 | ||||||||
\(646\) | 1.84201e9 | 0.268831 | ||||||||
\(647\) | 1.87158e9 | 0.271671 | 0.135835 | − | 0.990731i | \(-0.456628\pi\) | ||||
0.135835 | + | 0.990731i | \(0.456628\pi\) | |||||||
\(648\) | −8.33999e8 | −0.120407 | ||||||||
\(649\) | 1.02651e9 | 0.147403 | ||||||||
\(650\) | −3.06321e8 | −0.0437501 | ||||||||
\(651\) | −3.76405e9 | −0.534715 | ||||||||
\(652\) | −6.88648e8 | −0.0973040 | ||||||||
\(653\) | −9.58524e9 | −1.34712 | −0.673561 | − | 0.739132i | \(-0.735236\pi\) | ||||
−0.673561 | + | 0.739132i | \(0.735236\pi\) | |||||||
\(654\) | 2.38987e9 | 0.334081 | ||||||||
\(655\) | 7.43196e9 | 1.03338 | ||||||||
\(656\) | 4.34747e9 | 0.601276 | ||||||||
\(657\) | 1.91059e9 | 0.262839 | ||||||||
\(658\) | 1.70663e8 | 0.0233533 | ||||||||
\(659\) | −1.22998e10 | −1.67417 | −0.837087 | − | 0.547070i | \(-0.815743\pi\) | ||||
−0.837087 | + | 0.547070i | \(0.815743\pi\) | |||||||
\(660\) | −1.43585e9 | −0.194405 | ||||||||
\(661\) | 1.28794e9 | 0.173456 | 0.0867280 | − | 0.996232i | \(-0.472359\pi\) | ||||
0.0867280 | + | 0.996232i | \(0.472359\pi\) | |||||||
\(662\) | −4.67206e9 | −0.625900 | ||||||||
\(663\) | −3.25877e8 | −0.0434267 | ||||||||
\(664\) | 8.84985e9 | 1.17313 | ||||||||
\(665\) | −5.84579e9 | −0.770845 | ||||||||
\(666\) | 1.44879e9 | 0.190041 | ||||||||
\(667\) | 1.15401e10 | 1.50581 | ||||||||
\(668\) | 1.45800e9 | 0.189252 | ||||||||
\(669\) | −1.72525e9 | −0.222772 | ||||||||
\(670\) | 6.87411e9 | 0.882988 | ||||||||
\(671\) | 1.27419e10 | 1.62818 | ||||||||
\(672\) | −2.36272e9 | −0.300345 | ||||||||
\(673\) | 9.85741e8 | 0.124655 | 0.0623275 | − | 0.998056i | \(-0.480148\pi\) | ||||
0.0623275 | + | 0.998056i | \(0.480148\pi\) | |||||||
\(674\) | 3.30509e9 | 0.415789 | ||||||||
\(675\) | 5.01585e8 | 0.0627742 | ||||||||
\(676\) | 2.02387e9 | 0.251981 | ||||||||
\(677\) | −1.00272e10 | −1.24200 | −0.620999 | − | 0.783812i | \(-0.713273\pi\) | ||||
−0.620999 | + | 0.783812i | \(0.713273\pi\) | |||||||
\(678\) | 5.87426e9 | 0.723852 | ||||||||
\(679\) | −6.45703e9 | −0.791569 | ||||||||
\(680\) | −4.94208e9 | −0.602738 | ||||||||
\(681\) | 6.24536e9 | 0.757779 | ||||||||
\(682\) | 7.22344e9 | 0.871964 | ||||||||
\(683\) | −2.51763e8 | −0.0302356 | −0.0151178 | − | 0.999886i | \(-0.504812\pi\) | ||||
−0.0151178 | + | 0.999886i | \(0.504812\pi\) | |||||||
\(684\) | −4.65611e8 | −0.0556323 | ||||||||
\(685\) | −1.38801e10 | −1.64997 | ||||||||
\(686\) | 6.99378e9 | 0.827138 | ||||||||
\(687\) | −7.54116e9 | −0.887339 | ||||||||
\(688\) | −2.69479e8 | −0.0315475 | ||||||||
\(689\) | 2.81591e8 | 0.0327983 | ||||||||
\(690\) | 6.75813e9 | 0.783168 | ||||||||
\(691\) | 1.20798e10 | 1.39279 | 0.696396 | − | 0.717657i | \(-0.254786\pi\) | ||||
0.696396 | + | 0.717657i | \(0.254786\pi\) | |||||||
\(692\) | 2.19296e9 | 0.251570 | ||||||||
\(693\) | −3.42473e9 | −0.390895 | ||||||||
\(694\) | 9.53300e9 | 1.08261 | ||||||||
\(695\) | 6.35460e9 | 0.718028 | ||||||||
\(696\) | −6.12707e9 | −0.688844 | ||||||||
\(697\) | −3.84569e9 | −0.430189 | ||||||||
\(698\) | −2.30396e9 | −0.256437 | ||||||||
\(699\) | 6.03477e9 | 0.668329 | ||||||||
\(700\) | 7.91746e8 | 0.0872455 | ||||||||
\(701\) | 1.78453e10 | 1.95664 | 0.978321 | − | 0.207096i | \(-0.0664013\pi\) | ||||
0.978321 | + | 0.207096i | \(0.0664013\pi\) | |||||||
\(702\) | −2.36600e8 | −0.0258127 | ||||||||
\(703\) | 3.94093e9 | 0.427814 | ||||||||
\(704\) | 1.16101e10 | 1.25410 | ||||||||
\(705\) | −1.61947e8 | −0.0174065 | ||||||||
\(706\) | −1.56957e9 | −0.167866 | ||||||||
\(707\) | −2.24325e9 | −0.238732 | ||||||||
\(708\) | −1.83299e8 | −0.0194109 | ||||||||
\(709\) | −6.60811e9 | −0.696331 | −0.348165 | − | 0.937433i | \(-0.613195\pi\) | ||||
−0.348165 | + | 0.937433i | \(0.613195\pi\) | |||||||
\(710\) | −1.00213e10 | −1.05080 | ||||||||
\(711\) | −2.13865e9 | −0.223149 | ||||||||
\(712\) | −1.27293e10 | −1.32167 | ||||||||
\(713\) | 1.18367e10 | 1.22298 | ||||||||
\(714\) | −2.41932e9 | −0.248742 | ||||||||
\(715\) | −1.98469e9 | −0.203059 | ||||||||
\(716\) | 3.91733e9 | 0.398836 | ||||||||
\(717\) | 2.00607e9 | 0.203249 | ||||||||
\(718\) | −1.07521e10 | −1.08407 | ||||||||
\(719\) | 1.04223e10 | 1.04572 | 0.522859 | − | 0.852419i | \(-0.324866\pi\) | ||||
0.522859 | + | 0.852419i | \(0.324866\pi\) | |||||||
\(720\) | −2.59531e9 | −0.259135 | ||||||||
\(721\) | 1.01470e10 | 1.00824 | ||||||||
\(722\) | −5.07200e9 | −0.501532 | ||||||||
\(723\) | −4.30419e9 | −0.423553 | ||||||||
\(724\) | 1.78826e9 | 0.175124 | ||||||||
\(725\) | 3.68495e9 | 0.359128 | ||||||||
\(726\) | 1.44545e9 | 0.140192 | ||||||||
\(727\) | −1.07207e10 | −1.03479 | −0.517394 | − | 0.855747i | \(-0.673098\pi\) | ||||
−0.517394 | + | 0.855747i | \(0.673098\pi\) | |||||||
\(728\) | −1.81966e9 | −0.174795 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | 8.22002e9 | 0.782065 | ||||||||
\(731\) | 2.38375e8 | 0.0225710 | ||||||||
\(732\) | −2.27525e9 | −0.214408 | ||||||||
\(733\) | 2.61994e9 | 0.245712 | 0.122856 | − | 0.992424i | \(-0.460795\pi\) | ||||
0.122856 | + | 0.992424i | \(0.460795\pi\) | |||||||
\(734\) | −1.40350e9 | −0.131001 | ||||||||
\(735\) | 5.20653e8 | 0.0483663 | ||||||||
\(736\) | 7.42999e9 | 0.686935 | ||||||||
\(737\) | 1.09545e10 | 1.00799 | ||||||||
\(738\) | −2.79212e9 | −0.255704 | ||||||||
\(739\) | 1.57747e10 | 1.43783 | 0.718913 | − | 0.695100i | \(-0.244640\pi\) | ||||
0.718913 | + | 0.695100i | \(0.244640\pi\) | |||||||
\(740\) | −2.17011e9 | −0.196866 | ||||||||
\(741\) | −6.43585e8 | −0.0581088 | ||||||||
\(742\) | 2.09054e9 | 0.187864 | ||||||||
\(743\) | −942965. | −8.43402e−5 0 | −4.21701e−5 | − | 1.00000i | \(-0.500013\pi\) | ||||
−4.21701e−5 | 1.00000i | \(0.500013\pi\) | ||||||||
\(744\) | −6.28456e9 | −0.559460 | ||||||||
\(745\) | −1.85539e10 | −1.64395 | ||||||||
\(746\) | 1.03824e10 | 0.915617 | ||||||||
\(747\) | −4.11105e9 | −0.360854 | ||||||||
\(748\) | −1.61641e9 | −0.141220 | ||||||||
\(749\) | 6.90463e9 | 0.600418 | ||||||||
\(750\) | −4.45787e9 | −0.385845 | ||||||||
\(751\) | −1.30768e10 | −1.12658 | −0.563288 | − | 0.826261i | \(-0.690464\pi\) | ||||
−0.563288 | + | 0.826261i | \(0.690464\pi\) | |||||||
\(752\) | 2.06100e8 | 0.0176732 | ||||||||
\(753\) | −3.00279e9 | −0.256296 | ||||||||
\(754\) | −1.73821e9 | −0.147673 | ||||||||
\(755\) | 9.89755e9 | 0.836976 | ||||||||
\(756\) | 6.11539e8 | 0.0514752 | ||||||||
\(757\) | 2.15132e10 | 1.80247 | 0.901237 | − | 0.433326i | \(-0.142660\pi\) | ||||
0.901237 | + | 0.433326i | \(0.142660\pi\) | |||||||
\(758\) | 1.45320e10 | 1.21195 | ||||||||
\(759\) | 1.07697e10 | 0.894038 | ||||||||
\(760\) | −9.76027e9 | −0.806519 | ||||||||
\(761\) | −1.50838e10 | −1.24069 | −0.620347 | − | 0.784328i | \(-0.713008\pi\) | ||||
−0.620347 | + | 0.784328i | \(0.713008\pi\) | |||||||
\(762\) | −1.70460e9 | −0.139566 | ||||||||
\(763\) | −8.53820e9 | −0.695874 | ||||||||
\(764\) | −2.88757e9 | −0.234264 | ||||||||
\(765\) | 2.29576e9 | 0.185401 | ||||||||
\(766\) | −1.45484e10 | −1.16954 | ||||||||
\(767\) | −2.53363e8 | −0.0202749 | ||||||||
\(768\) | −5.20838e9 | −0.414895 | ||||||||
\(769\) | −2.21876e9 | −0.175941 | −0.0879707 | − | 0.996123i | \(-0.528038\pi\) | ||||
−0.0879707 | + | 0.996123i | \(0.528038\pi\) | |||||||
\(770\) | −1.47344e10 | −1.16309 | ||||||||
\(771\) | −3.45113e9 | −0.271188 | ||||||||
\(772\) | 6.82804e6 | 0.000534116 0 | ||||||||
\(773\) | −8.81943e9 | −0.686771 | −0.343386 | − | 0.939194i | \(-0.611574\pi\) | ||||
−0.343386 | + | 0.939194i | \(0.611574\pi\) | |||||||
\(774\) | 1.73070e8 | 0.0134162 | ||||||||
\(775\) | 3.77967e9 | 0.291674 | ||||||||
\(776\) | −1.07808e10 | −0.828202 | ||||||||
\(777\) | −5.17605e9 | −0.395845 | ||||||||
\(778\) | 7.14431e9 | 0.543916 | ||||||||
\(779\) | −7.59497e9 | −0.575632 | ||||||||
\(780\) | 3.54397e8 | 0.0267398 | ||||||||
\(781\) | −1.59697e10 | −1.19955 | ||||||||
\(782\) | 7.60796e9 | 0.568912 | ||||||||
\(783\) | 2.84623e9 | 0.211887 | ||||||||
\(784\) | −6.62603e8 | −0.0491074 | ||||||||
\(785\) | 1.91895e9 | 0.141586 | ||||||||
\(786\) | 6.07443e9 | 0.446197 | ||||||||
\(787\) | −1.26134e10 | −0.922406 | −0.461203 | − | 0.887295i | \(-0.652582\pi\) | ||||
−0.461203 | + | 0.887295i | \(0.652582\pi\) | |||||||
\(788\) | 3.53341e9 | 0.257248 | ||||||||
\(789\) | 9.11663e9 | 0.660792 | ||||||||
\(790\) | −9.20119e9 | −0.663971 | ||||||||
\(791\) | −2.09868e10 | −1.50775 | ||||||||
\(792\) | −5.71802e9 | −0.408985 | ||||||||
\(793\) | −3.14494e9 | −0.223952 | ||||||||
\(794\) | −2.03905e10 | −1.44562 | ||||||||
\(795\) | −1.98377e9 | −0.140025 | ||||||||
\(796\) | 2.37760e9 | 0.167087 | ||||||||
\(797\) | 2.61316e9 | 0.182836 | 0.0914179 | − | 0.995813i | \(-0.470860\pi\) | ||||
0.0914179 | + | 0.995813i | \(0.470860\pi\) | |||||||
\(798\) | −4.77799e9 | −0.332840 | ||||||||
\(799\) | −1.82312e8 | −0.0126445 | ||||||||
\(800\) | 2.37253e9 | 0.163831 | ||||||||
\(801\) | 5.91318e9 | 0.406544 | ||||||||
\(802\) | −1.27450e10 | −0.872429 | ||||||||
\(803\) | 1.30993e10 | 0.892779 | ||||||||
\(804\) | −1.95609e9 | −0.132737 | ||||||||
\(805\) | −2.41445e10 | −1.63130 | ||||||||
\(806\) | −1.78289e9 | −0.119936 | ||||||||
\(807\) | −1.00012e10 | −0.669876 | ||||||||
\(808\) | −3.74539e9 | −0.249780 | ||||||||
\(809\) | −2.83771e10 | −1.88429 | −0.942147 | − | 0.335199i | \(-0.891196\pi\) | ||||
−0.942147 | + | 0.335199i | \(0.891196\pi\) | |||||||
\(810\) | 1.66681e9 | 0.110202 | ||||||||
\(811\) | −2.32326e10 | −1.52941 | −0.764705 | − | 0.644380i | \(-0.777115\pi\) | ||||
−0.764705 | + | 0.644380i | \(0.777115\pi\) | |||||||
\(812\) | 4.49274e9 | 0.294487 | ||||||||
\(813\) | 6.33935e9 | 0.413740 | ||||||||
\(814\) | 9.93315e9 | 0.645508 | ||||||||
\(815\) | 6.70584e9 | 0.433912 | ||||||||
\(816\) | −2.92168e9 | −0.188242 | ||||||||
\(817\) | 4.70775e8 | 0.0302020 | ||||||||
\(818\) | 2.67458e10 | 1.70851 | ||||||||
\(819\) | 8.45291e8 | 0.0537666 | ||||||||
\(820\) | 4.18225e9 | 0.264887 | ||||||||
\(821\) | 1.23630e10 | 0.779691 | 0.389845 | − | 0.920880i | \(-0.372528\pi\) | ||||
0.389845 | + | 0.920880i | \(0.372528\pi\) | |||||||
\(822\) | −1.13448e10 | −0.712433 | ||||||||
\(823\) | 1.47567e10 | 0.922763 | 0.461382 | − | 0.887202i | \(-0.347354\pi\) | ||||
0.461382 | + | 0.887202i | \(0.347354\pi\) | |||||||
\(824\) | 1.69417e10 | 1.05490 | ||||||||
\(825\) | 3.43894e9 | 0.213224 | ||||||||
\(826\) | −1.88097e9 | −0.116132 | ||||||||
\(827\) | 7.08701e9 | 0.435706 | 0.217853 | − | 0.975982i | \(-0.430095\pi\) | ||||
0.217853 | + | 0.975982i | \(0.430095\pi\) | |||||||
\(828\) | −1.92309e9 | −0.117732 | ||||||||
\(829\) | −5.40146e7 | −0.00329284 | −0.00164642 | − | 0.999999i | \(-0.500524\pi\) | ||||
−0.00164642 | + | 0.999999i | \(0.500524\pi\) | |||||||
\(830\) | −1.76872e10 | −1.07370 | ||||||||
\(831\) | −4.19219e9 | −0.253418 | ||||||||
\(832\) | −2.86561e9 | −0.172498 | ||||||||
\(833\) | 5.86126e8 | 0.0351345 | ||||||||
\(834\) | 5.19386e9 | 0.310034 | ||||||||
\(835\) | −1.41976e10 | −0.843940 | ||||||||
\(836\) | −3.19230e9 | −0.188965 | ||||||||
\(837\) | 2.91939e9 | 0.172089 | ||||||||
\(838\) | −6.34379e8 | −0.0372387 | ||||||||
\(839\) | −4.08313e9 | −0.238686 | −0.119343 | − | 0.992853i | \(-0.538079\pi\) | ||||
−0.119343 | + | 0.992853i | \(0.538079\pi\) | |||||||
\(840\) | 1.28192e10 | 0.746251 | ||||||||
\(841\) | 3.66030e9 | 0.212193 | ||||||||
\(842\) | 1.45032e10 | 0.837283 | ||||||||
\(843\) | −3.11146e9 | −0.178883 | ||||||||
\(844\) | 5.43771e9 | 0.311328 | ||||||||
\(845\) | −1.97078e10 | −1.12367 | ||||||||
\(846\) | −1.32365e8 | −0.00751586 | ||||||||
\(847\) | −5.16410e9 | −0.292013 | ||||||||
\(848\) | 2.52462e9 | 0.142171 | ||||||||
\(849\) | 1.20172e10 | 0.673949 | ||||||||
\(850\) | 2.42936e9 | 0.135683 | ||||||||
\(851\) | 1.62770e10 | 0.905359 | ||||||||
\(852\) | 2.85164e9 | 0.157963 | ||||||||
\(853\) | 4.28167e8 | 0.0236207 | 0.0118103 | − | 0.999930i | \(-0.496241\pi\) | ||||
0.0118103 | + | 0.999930i | \(0.496241\pi\) | |||||||
\(854\) | −2.33481e10 | −1.28277 | ||||||||
\(855\) | 4.53398e9 | 0.248083 | ||||||||
\(856\) | 1.15281e10 | 0.628205 | ||||||||
\(857\) | −7.39852e9 | −0.401524 | −0.200762 | − | 0.979640i | \(-0.564342\pi\) | ||||
−0.200762 | + | 0.979640i | \(0.564342\pi\) | |||||||
\(858\) | −1.62216e9 | −0.0876777 | ||||||||
\(859\) | −2.72977e9 | −0.146943 | −0.0734717 | − | 0.997297i | \(-0.523408\pi\) | ||||
−0.0734717 | + | 0.997297i | \(0.523408\pi\) | |||||||
\(860\) | −2.59237e8 | −0.0138980 | ||||||||
\(861\) | 9.97531e9 | 0.532618 | ||||||||
\(862\) | 1.80274e10 | 0.958642 | ||||||||
\(863\) | 1.38149e10 | 0.731663 | 0.365832 | − | 0.930681i | \(-0.380785\pi\) | ||||
0.365832 | + | 0.930681i | \(0.380785\pi\) | |||||||
\(864\) | 1.83252e9 | 0.0966609 | ||||||||
\(865\) | −2.13543e10 | −1.12184 | ||||||||
\(866\) | 6.01268e9 | 0.314598 | ||||||||
\(867\) | −8.49469e9 | −0.442671 | ||||||||
\(868\) | 4.60822e9 | 0.239174 | ||||||||
\(869\) | −1.46629e10 | −0.757968 | ||||||||
\(870\) | 1.22455e10 | 0.630460 | ||||||||
\(871\) | −2.70378e9 | −0.138646 | ||||||||
\(872\) | −1.42556e10 | −0.728078 | ||||||||
\(873\) | 5.00806e9 | 0.254753 | ||||||||
\(874\) | 1.50252e10 | 0.761255 | ||||||||
\(875\) | 1.59265e10 | 0.803695 | ||||||||
\(876\) | −2.33908e9 | −0.117566 | ||||||||
\(877\) | 2.96899e10 | 1.48631 | 0.743157 | − | 0.669117i | \(-0.233327\pi\) | ||||
0.743157 | + | 0.669117i | \(0.233327\pi\) | |||||||
\(878\) | −7.25354e9 | −0.361675 | ||||||||
\(879\) | 1.97783e10 | 0.982264 | ||||||||
\(880\) | −1.77939e10 | −0.880200 | ||||||||
\(881\) | −3.95312e10 | −1.94771 | −0.973855 | − | 0.227169i | \(-0.927053\pi\) | ||||
−0.973855 | + | 0.227169i | \(0.927053\pi\) | |||||||
\(882\) | 4.25550e8 | 0.0208839 | ||||||||
\(883\) | −6.41631e9 | −0.313634 | −0.156817 | − | 0.987628i | \(-0.550123\pi\) | ||||
−0.156817 | + | 0.987628i | \(0.550123\pi\) | |||||||
\(884\) | 3.98962e8 | 0.0194244 | ||||||||
\(885\) | 1.78491e9 | 0.0865596 | ||||||||
\(886\) | −1.50128e10 | −0.725177 | ||||||||
\(887\) | −3.07401e10 | −1.47901 | −0.739507 | − | 0.673149i | \(-0.764941\pi\) | ||||
−0.739507 | + | 0.673149i | \(0.764941\pi\) | |||||||
\(888\) | −8.64207e9 | −0.414164 | ||||||||
\(889\) | 6.08997e9 | 0.290710 | ||||||||
\(890\) | 2.54405e10 | 1.20965 | ||||||||
\(891\) | 2.65621e9 | 0.125803 | ||||||||
\(892\) | 2.11217e9 | 0.0996441 | ||||||||
\(893\) | −3.60053e8 | −0.0169195 | ||||||||
\(894\) | −1.51648e10 | −0.709834 | ||||||||
\(895\) | −3.81457e10 | −1.77855 | ||||||||
\(896\) | −1.00733e10 | −0.467835 | ||||||||
\(897\) | −2.65816e9 | −0.122973 | ||||||||
\(898\) | −3.13474e9 | −0.144455 | ||||||||
\(899\) | 2.14476e10 | 0.984511 | ||||||||
\(900\) | −6.14076e8 | −0.0280785 | ||||||||
\(901\) | −2.23323e9 | −0.101718 | ||||||||
\(902\) | −1.91432e10 | −0.868544 | ||||||||
\(903\) | −6.18321e8 | −0.0279452 | ||||||||
\(904\) | −3.50401e10 | −1.57752 | ||||||||
\(905\) | −1.74136e10 | −0.780940 | ||||||||
\(906\) | 8.08965e9 | 0.361394 | ||||||||
\(907\) | 6.93998e9 | 0.308839 | 0.154420 | − | 0.988005i | \(-0.450649\pi\) | ||||
0.154420 | + | 0.988005i | \(0.450649\pi\) | |||||||
\(908\) | −7.64601e9 | −0.338949 | ||||||||
\(909\) | 1.73986e9 | 0.0768317 | ||||||||
\(910\) | 3.63673e9 | 0.159980 | ||||||||
\(911\) | 1.43108e10 | 0.627118 | 0.313559 | − | 0.949569i | \(-0.398479\pi\) | ||||
0.313559 | + | 0.949569i | \(0.398479\pi\) | |||||||
\(912\) | −5.77011e9 | −0.251885 | ||||||||
\(913\) | −2.81860e10 | −1.22570 | ||||||||
\(914\) | −1.60376e10 | −0.694749 | ||||||||
\(915\) | 2.21557e10 | 0.956118 | ||||||||
\(916\) | 9.23243e9 | 0.396901 | ||||||||
\(917\) | −2.17019e10 | −0.929405 | ||||||||
\(918\) | 1.87642e9 | 0.0800534 | ||||||||
\(919\) | 4.66570e10 | 1.98295 | 0.991477 | − | 0.130280i | \(-0.0415876\pi\) | ||||
0.991477 | + | 0.130280i | \(0.0415876\pi\) | |||||||
\(920\) | −4.03123e10 | −1.70679 | ||||||||
\(921\) | −7.01652e8 | −0.0295947 | ||||||||
\(922\) | 1.81459e10 | 0.762467 | ||||||||
\(923\) | 3.94165e9 | 0.164995 | ||||||||
\(924\) | 4.19280e9 | 0.174845 | ||||||||
\(925\) | 5.19753e9 | 0.215924 | ||||||||
\(926\) | 1.26697e10 | 0.524359 | ||||||||
\(927\) | −7.86999e9 | −0.324485 | ||||||||
\(928\) | 1.34628e10 | 0.552992 | ||||||||
\(929\) | −2.83056e10 | −1.15829 | −0.579146 | − | 0.815224i | \(-0.696614\pi\) | ||||
−0.579146 | + | 0.815224i | \(0.696614\pi\) | |||||||
\(930\) | 1.25602e10 | 0.512043 | ||||||||
\(931\) | 1.15756e9 | 0.0470131 | ||||||||
\(932\) | −7.38819e9 | −0.298939 | ||||||||
\(933\) | 2.08434e10 | 0.840199 | ||||||||
\(934\) | 2.14138e10 | 0.859962 | ||||||||
\(935\) | 1.57401e10 | 0.629748 | ||||||||
\(936\) | 1.41132e9 | 0.0562548 | ||||||||
\(937\) | 7.53166e9 | 0.299090 | 0.149545 | − | 0.988755i | \(-0.452219\pi\) | ||||
0.149545 | + | 0.988755i | \(0.452219\pi\) | |||||||
\(938\) | −2.00729e10 | −0.794147 | ||||||||
\(939\) | −1.39815e10 | −0.551093 | ||||||||
\(940\) | 1.98267e8 | 0.00778579 | ||||||||
\(941\) | −2.80301e10 | −1.09663 | −0.548316 | − | 0.836271i | \(-0.684731\pi\) | ||||
−0.548316 | + | 0.836271i | \(0.684731\pi\) | |||||||
\(942\) | 1.56843e9 | 0.0611347 | ||||||||
\(943\) | −3.13691e10 | −1.21818 | ||||||||
\(944\) | −2.27155e9 | −0.0878860 | ||||||||
\(945\) | −5.95497e9 | −0.229545 | ||||||||
\(946\) | 1.18659e9 | 0.0455704 | ||||||||
\(947\) | 5.03691e10 | 1.92725 | 0.963627 | − | 0.267250i | \(-0.0861150\pi\) | ||||
0.963627 | + | 0.267250i | \(0.0861150\pi\) | |||||||
\(948\) | 2.61828e9 | 0.0998131 | ||||||||
\(949\) | −3.23317e9 | −0.122799 | ||||||||
\(950\) | 4.79781e9 | 0.181556 | ||||||||
\(951\) | 1.52212e10 | 0.573876 | ||||||||
\(952\) | 1.44313e10 | 0.542095 | ||||||||
\(953\) | −1.09520e10 | −0.409890 | −0.204945 | − | 0.978773i | \(-0.565702\pi\) | ||||
−0.204945 | + | 0.978773i | \(0.565702\pi\) | |||||||
\(954\) | −1.62141e9 | −0.0604609 | ||||||||
\(955\) | 2.81182e10 | 1.04466 | ||||||||
\(956\) | −2.45597e9 | −0.0909118 | ||||||||
\(957\) | 1.95142e10 | 0.719712 | ||||||||
\(958\) | −4.03137e10 | −1.48140 | ||||||||
\(959\) | 4.05310e10 | 1.48396 | ||||||||
\(960\) | 2.01878e10 | 0.736445 | ||||||||
\(961\) | −5.51371e9 | −0.200407 | ||||||||
\(962\) | −2.45170e9 | −0.0887879 | ||||||||
\(963\) | −5.35521e9 | −0.193234 | ||||||||
\(964\) | 5.26950e9 | 0.189452 | ||||||||
\(965\) | −6.64893e7 | −0.00238181 | ||||||||
\(966\) | −1.97343e10 | −0.704370 | ||||||||
\(967\) | −1.15786e10 | −0.411778 | −0.205889 | − | 0.978575i | \(-0.566009\pi\) | ||||
−0.205889 | + | 0.978575i | \(0.566009\pi\) | |||||||
\(968\) | −8.62211e9 | −0.305527 | ||||||||
\(969\) | 5.10412e9 | 0.180214 | ||||||||
\(970\) | 2.15464e10 | 0.758007 | ||||||||
\(971\) | −2.02758e10 | −0.710739 | −0.355370 | − | 0.934726i | \(-0.615645\pi\) | ||||
−0.355370 | + | 0.934726i | \(0.615645\pi\) | |||||||
\(972\) | −4.74308e8 | −0.0165664 | ||||||||
\(973\) | −1.85559e10 | −0.645784 | ||||||||
\(974\) | 4.93290e10 | 1.71059 | ||||||||
\(975\) | −8.48798e8 | −0.0293284 | ||||||||
\(976\) | −2.81962e10 | −0.970769 | ||||||||
\(977\) | −1.76622e10 | −0.605917 | −0.302958 | − | 0.953004i | \(-0.597974\pi\) | ||||
−0.302958 | + | 0.953004i | \(0.597974\pi\) | |||||||
\(978\) | 5.48094e9 | 0.187357 | ||||||||
\(979\) | 4.05417e10 | 1.38090 | ||||||||
\(980\) | −6.37421e8 | −0.0216339 | ||||||||
\(981\) | 6.62220e9 | 0.223955 | ||||||||
\(982\) | 5.16188e9 | 0.173947 | ||||||||
\(983\) | 5.25893e10 | 1.76588 | 0.882938 | − | 0.469489i | \(-0.155562\pi\) | ||||
0.882938 | + | 0.469489i | \(0.155562\pi\) | |||||||
\(984\) | 1.66550e10 | 0.557266 | ||||||||
\(985\) | −3.44073e10 | −1.14716 | ||||||||
\(986\) | 1.37853e10 | 0.457981 | ||||||||
\(987\) | 4.72898e8 | 0.0156551 | ||||||||
\(988\) | 7.87923e8 | 0.0259917 | ||||||||
\(989\) | 1.94442e9 | 0.0639149 | ||||||||
\(990\) | 1.14279e10 | 0.374321 | ||||||||
\(991\) | −2.06461e10 | −0.673876 | −0.336938 | − | 0.941527i | \(-0.609391\pi\) | ||||
−0.336938 | + | 0.941527i | \(0.609391\pi\) | |||||||
\(992\) | 1.38089e10 | 0.449125 | ||||||||
\(993\) | −1.29460e10 | −0.419579 | ||||||||
\(994\) | 2.92629e10 | 0.945071 | ||||||||
\(995\) | −2.31523e10 | −0.745097 | ||||||||
\(996\) | 5.03304e9 | 0.161407 | ||||||||
\(997\) | −2.76691e9 | −0.0884224 | −0.0442112 | − | 0.999022i | \(-0.514077\pi\) | ||||
−0.0442112 | + | 0.999022i | \(0.514077\pi\) | |||||||
\(998\) | 1.11887e10 | 0.356304 | ||||||||
\(999\) | 4.01453e9 | 0.127396 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 177.8.a.d.1.12 | ✓ | 18 | |
3.2 | odd | 2 | 531.8.a.e.1.7 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.8.a.d.1.12 | ✓ | 18 | 1.1 | even | 1 | trivial | |
531.8.a.e.1.7 | 18 | 3.2 | odd | 2 |